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It's not clear (yet) what a 100% clean energy powered world would use to cover the last couple of percent of demand when loads peak and/or variable generation troughs for extended periods.

It'll be some combination of demand management (which isn't nearly as horrifying as people make it out to be), pumped hydro, long-duration batteries like iron-air, but also possibly burning hydrogen or hydrogen-derived synthetic fuels (produced by electrolysis when hydrogen is abundant) and/or biofuels in turbines.


Somebody calculated that a home in UK needs 1 Megawatt-Hour battery to backup solar energy during the winter. I suspect in 10 years that may cost below 25K, a small fraction of the property cost.
But is it really 1 MWh of _electricity_, or could you replace a good chunk of that with a huge tank of boiling water? In the winter, about half of my electricity consumption goes to my heat pump, to produce 45-50C water for heating and tap water. But if we could increase the reservoir temperature to 95C (or even go superheated to 160C at 6 bar), then it could supply the 45-50C flow temperature much longer without needing to recharge.
In cold places district heating solutions with seasonal storage, like this one, make a lot of sense:

https://www.vantaanenergia.fi/en/about-us/projects/varanto-t...

That's probably assuming a solar system sized to cover typical summer energy usage. You can simply over-provision solar until you have wasted capacity in summer and little to no storage requirement in winter. Then it's just a tradeoff between battery and solar costs to find the best price point.

Also this calculation probably assumes no baseload power imported from the grid, where means such as wind and tidal power work year-round and help offset the need for batteries.

The UK is very far north and very windy. I suggest a smaller battery and a wind turbine.
There is a time- honored, straightforward way to deal with the last two percent problem, which is to overbuild by a couple of percent or so.
That’s not how the maths works unfortunately.

Basically, you end up having to overbuild to crazy levels, or build insane amounts of battery storage, which only gets used a few days a year.

That is right (if rather exaggerated, and I will note that it was you who originally picked the figure of two percent), and in practice, we accept a certain risk that we will not always have all the capacity we want, even though (or because) we cannot precisely predict how big or often these events will be. There is no particular reason to think this specific case is any different.
Why can't we predict how big or how often those events would be? We have clear understandings of the distribution of probabilities for all kinds of weather scenarios - see for example 1-50/100/1000 year flood/droughts.
I'm not saying we cannot do it, just that we cannot always get it right, and there is plenty of empirical evidence for that.

The second point is that the distribution has a long tail, especially when we consider the possibility of multiple independent incidents overlapping in time, to the point where it becomes infeasible to suppose that we could be prepared to continue operating as if nothing had happened in all conceivable scenarios, regardless of how accurately we could predict their likelihood.

We can and do, and there are detailed plans based on those weather scenarios (eg for the Australian east coast grid; there is AEMO’s Integrated System Plan).

Things in the US are a bit more of a mixed bag, for better or worse, but there have been studies done that suggest that you can get very high renewables levels cost effectively, but not to 100% without new technology (eg “clean firm” power like geothermal, new nuclear being something other than a clusterfumble, long-term storage like iron-air batteries, etc etc etc).

The problem is the last two percent isn't evenly distributed in time, but rather occurs rarely, but in large chunks. On average it's 2%, but not at each point in time.

Also, if solar ends up much cheaper than wind there's going to be need for seasonal energy storage, which could be considerably more than 2% at high latitude. Batteries are unsuitable for this.

Or very long term thermal storage, as from standardthermal.com

This would also need some sort of turbine to convert back to electrical energy.

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